Extended S-supplement submodules

Authors: YILMAZ DURĞUN

Abstract: In this paper, we introduced and studied extended S-supplement submodules. A submodule U of a module V is called extended S-supplement submodule in V if there exists a submodule T of V such that V = T + U and U ∩ T is Goldie torsion. Extended S-supplement submodule is a dual notion of extended S-closed submodule. The class of extended S-supplement sequences is a proper class which is generated by nonsingular modules injectively. We studied coinjective objects of this class. Moreover, extended S-supplemented modules are also investigated. We present new characterizations of Z₂(R_R) -semiperfect rings and SI-rings by extended S-supplement submodules.

Keywords: S-supplement submodules, Goldie torsion theory, coinjective modules

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